{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `Probability Density function for heights` 🚀  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:241: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np  \n",
    "import scipy.stats as stats \n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "# Set the mean (mu) and std dev (sigma) for the normal distribution\n",
    "mu, sigma = 170, 10  \n",
    "x = np.linspace(140, 200, 100) \n",
    "\n",
    "# Calculate the (PDF) for the normal distribution\n",
    "pdf = stats.norm.pdf(x, mu, sigma)  \n",
    "\n",
    "plt.figure(figsize=(5, 4))  \n",
    "plt.plot(x, pdf, color='r')  \n",
    "plt.xlabel('Height (cm)')  \n",
    "plt.ylabel('Density')  \n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating probability for height in a range! \n",
    "We find the cumulative distribution function got 180 & 160. <br> Here's the formula for cdf ⬇️ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$F(x) = P(X \\leq x) = \\int_{-\\infty}^{x} f(t) dt$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(160 <= Height <= 180) = 0.6827\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "\n",
    "mu, sigma = 170, 10\n",
    "\n",
    "# Calculate the CDF values for the range limits\n",
    "cdf_lower = stats.norm.cdf(160, mu, sigma)\n",
    "cdf_upper = stats.norm.cdf(180, mu, sigma)\n",
    "\n",
    "# Subtract the CDF values to find the probability within the range\n",
    "probability = cdf_upper - cdf_lower\n",
    "\n",
    "print(f\"P(160 <= Height <= 180) = {probability:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "env_twitter",
   "language": "python",
   "name": "env_twitter"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
